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No. The Principled BSDF shader is a combination of several other shaders, but it is not a replacement for them. From the Blender Manual:

It is based on the Disney principled model also known as the “PBR” shader, making it compatible with other software such as Pixar’s Renderman® and Unreal Engine®. Image textures painted or baked from software like Substance Painter® may be directly linked to the corresponding parameters in this shader

None of the current nodes are obsolete or deprecated. There are, however, two main advantages to this shader:

First, as you pointed out, it is a combination of the other shaders, using physically based formulae. This means that we can plug is colors and values without having to worry whether or not what we are creating looks realistic. (This means that it has built-in Fresnel).

This second advantage is that it uses Disney's standardized shading model, making it so that results with Cycles should match up with results in Renderman, Unreal and Substance Painter. This can save a lot of time, especially for someone who switches between software.

It isn't a replacement for any nodes, though, since it might be faster or simpler to just use more basic nodes.

Of the 16 other shading nodes (not including Add, Mix, and Principled), these 5 can be replicated with Principled BSDF:

Anisotropic BSDF

Diffuse BSDF

Glass BSDF (called Transmission)

Glossy BSDF (called Specular)

Subsurface Scattering1

Principled BSDF does not cover any Volumetric shaders, transparencies other than Glass, or more specialized effects like Velvet2, Toon, Ambient Occlusion, or Hair.

1 While this does simulate Subsurface Scattering, it does not use the same algorithms as the Cycles Subsurface Scattering node, see this answer.

2 The sheen property is meant to simulate cloth, and so is similar to the Velvet shader. The Velvet shader has more options though (and I assume slightly different equations), so I wouldn't consider it an exact duplicate.

$\begingroup$"Replacement" is not the right word, I should've used "alternative". Like you said, a Principled shader with 100% sheen looks different than a Velvet shader, that alone justifies choosing one over the other (the final result).$\endgroup$
– R. NavegaOct 19 '17 at 0:02